A271324 a(n) = n + floor(n/4) + (n mod 4).

0, 2, 4, 6, 5, 7, 9, 11, 10, 12, 14, 16, 15, 17, 19, 21, 20, 22, 24, 26, 25, 27, 29, 31, 30, 32, 34, 36, 35, 37, 39, 41, 40, 42, 44, 46, 45, 47, 49, 51, 50, 52, 54, 56, 55, 57, 59, 61, 60, 62, 64, 66, 65, 67, 69, 71, 70, 72, 74, 76, 75, 77, 79, 81, 80, 82, 84, 86, 85, 87, 89

Offset

0,2

Comments

Sort the terms in increasing order and add 1 to get sequence A032769.

Links

Bruno Berselli, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

Formula

O.g.f.: x*(2 + 2*x + 2*x^2 - x^3)/((1 - x)^2*(1 + x + x^2 + x^3)).

E.g.f.: ((6 + 5*x)*sinh(x) + (3 + 5*x)*cosh(x) - 3*(sin(x) + cos(x)))/4.

a(n) = 1 + (10*n - 6*(-1)^((n-1)*n/2) - 3*(-1)^n + 1)/8.

a(4*k + r) = 5*k + 2*r, with r = 0, 1, 2 or 3.

a(n + 4*k) = a(n) + 5*k.

Mathematica

Table[n + Floor[n/4] + Mod[n, 4], {n, 0, 80}]

Prog

(PARI) vector(80, n, n--; n + floor(n/4) + n%4)
(Sage) [n + floor(n/4) + n%4 for n in (0..80)]
(Maxima) makelist(n + floor(n/4) + mod(n, 4), n, 0, 80);
(Magma) [n + Floor(n/4) + (n mod 4): n in [0..80]];
(Python)
def A271324(n): return n+(n>>2)+(n&3) # Chai Wah Wu, Jan 29 2023

Crossrefs

Cf. A032769.

Cf. numbers of the form m + floor(m/k) + (m mod k): A028242 (k=-2), A000004 (k=-1), A005843 (k=1), A007494 (k=2), A063224 (k=3).

Sequence in context: A023825 A022485 A230631 * A177961 A353733 A297615

Adjacent sequences: A271321 A271322 A271323 * A271325 A271326 A271327

Keyword

nonn,easy

Author

Bruno Berselli, Apr 04 2016

Status

approved